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Approximations of set-valued functions by metric linear operators. (English) Zbl 1123.26024
The authors adapt linear approximation operators for real-valued functions, based on samples of the approximated function, to set-valued functions by replacing an operation between numbers with an operation between sets. They introduce approximation operators for univariante set-valued functions with general compact images in $$\mathbb{R}^n$$. Finally, as examples the authors study metric Bernstein operators, metric Schoenberg operators, and metric polynomial interpolants.

##### MSC:
 26E25 Set-valued functions 54C65 Selections in general topology
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